Probability of X wins in a row.

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to me you tried to answer the OP question as I did (you have done this before in the past and I know how sensitive you can be)

to me it looks like you are trying to get the average number of streaks. there is an easier way for that, but the OP did not ask that question.

averages can be used to calculate a probability but it takes way more math than you and I can do (I think integrating using calculus is one way?)

just hope the OP can find what he wants from our posts

(Quote Clipped)

I'm not being sensitive, in my post I referred several times to, "Initial spins." In other words, as soon as a loss happens it begins a new streak. The reason I believed that is what the OP wanted (it wasn't) is because he made reference to a betting system that I assumed was likely the Reverse Martingale.

Again, he was asking a different question which you answered extremely well, and that's perfectly fine with me. I don't know what the purpose of what I perceived as a condescending tone in your earlier post was all about, but any sensitivity that you're perceiving on my part is more likely as a response to the condescension rather than the mere possibility of being wrong. I'm wrong quite a bit of the time, and someone who knows better than I do often comes along and corrects my mistake, so I really have no issues with that happening.

Also, if it makes you happy, I probably wouldn't have known where to begin on the question that you did answer. Now I do know where to begin, so thank you for that.

Let's assume 50/50 odds for simplicity's sake, I can always substitute in 18/37 or whatever if I know the formula.

The probability of getting 8 reds in a row is .5 to the power of 8. So somewhere around .39% But that's just the probability of getting that result right now on the next 8 spins. With a 100 or 1000 spin sample size it would surely be higher, but I'm at a loss for how exactly to calculate it.

just an update and a FYI.at least 8 in a rowp=18/37spins 50: 0.0691883981827spins 100: 0.1421953754224spins 1000: 0.8028180750264all the above streak probabilities are only good before the 1st spin!

say you go 100 spins and NO streak of 8 hits.you are thinking"spins 1000: 0.8028180750264"this is not a correct thought at this point in time, unless you are thinking of the next 1000 spins.

there are 900 spins left out of the initial 1000 spinsspins 900: 0.7678258249610the probability has now lowered (as expected)

say you go 569 spins and NO streak of 8 hits.you are thinking"spins 1000: 0.8028180750264"

actually there are now 431 spins remainingspins 431: 0.5004782010791

it started out as about an 80% success ratenow it is down to a coin flip that it will not happen

That is a good reminder not to use the stats to start thinking the wheel will need to “catch up” with some streaks if there have not been any streaks for a while, etc. etc. That would be a gamblers fallacy, now wouldn’t it?

I’m looking at it more from a general risk assessment perspective.

For example: This is how much it’s going to cost me to play 1000 spins with no winning streak, and these are the odds of that happening (at the outset, as you said).

Not that any of this will ever change the house edge, but at least I know:

1. What the odds are of hitting my desired streak in a given session,2. What I will win if I hit it,3. What I will lose if I don’t hit it.

So I know roughly what I am getting myself into, and can plan my sessions accordingly.

Makes sense, no?

"The Quest stands upon the edge of a knife. Stray but a little, and it will fail, to the ruin of all."
- Elf Queen Galadriel, teaching Frodo about the importance of blackjack basic strategy.